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arXiv · 1112.4467

On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem

R. Mikulevicius·H. Pragarauskas
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Abstract

The existence and uniqueness in Sobolev spaces of solutions of the Cauchy problem to parabolic integro-differential equation of the order α\in(0,2) is investigated. The principal part of the operator has kernel m(t,x,y)/|y|^{d+α} with a bounded nondegenerate m, Hölder in x and measurable in y. The lower order part has bounded and measurable coefficients. The result is applied to prove the existence and uniqueness of the corresponding martingale problem.

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R. Mikulevicius, H. Pragarauskas. 2012-01-21. On the Cauchy problem for integro-differential operators in Sobolev classes and the martingale problem. https://arxiv.org/abs/1112.4467

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